The release included double the number of language arts and math questions that were made public last year. Education Commissioner John B. King, Jr., said the extra access aimed to help the public understand the breadth and depth of the Common Core standards that the new assessments were designed to measure.

Mr. King and the state Board of Regents have been staunch advocates for these standards, which supporters say are more clear, focused and rigorous than past expectations. Critics say the Common Core guidelines are too confusing and prescriptive, and they argue that teachers did not get enough training or textbooks to teach them since their adoption in 2010.

Some New York parents boycotted the tests this year, saying that pressure for results caused too much anxiety. In giving out the questions, Mr. King told educators that, “No one equates testing with teaching, and test prep should consume as little classroom time as possible.”

Test questions are expensive to create: the department asked the Legislature for $8.4 million this year to pay for a broader release to the public of questions for three years. That funding was denied, department officials said, so New York prints only four versions of each test (compared to more than 25 forms in Texas, for example) and has a smaller supply of questions for future exams.

The department also told districts the percentage of students that got each question right so educators can tailor instruction to their needs.